We present new estimates for the statistical properties of damped Lyman- \alpha absorbers ( DLAs ) .
We compute the column density distribution function at z > 2 , the line density , \mathrm { d } N / \mathrm { d } X , and the neutral hydrogen density , \Omega _ { \mathrm { DLA } } .
Our estimates are derived from the DLA catalogue of [ ] , which uses the SDSS–III DR12 quasar spectroscopic survey .
This catalogue provides a probability that a given spectrum contains a DLA .
It allows us to use even the noisiest data without biasing our results and thus substantially increases our sample size .
We measure a non-zero column density distribution function at 95 \% confidence for all column densities N _ { \mathrm { HI } } < 5 \times 10 ^ { 22 } cm ^ { -2 } .
We make the first measurements from SDSS of \mathrm { d } N / \mathrm { d } X and \Omega _ { \mathrm { DLA } } at z > 4 .
We show that our results are insensitive to the signal-to-noise ratio of the spectra , but that there is a residual dependence on quasar redshift for z < 2.5 , which may be due to remaining systematics in our analysis .